Support Vector Regression(SVR) SVR is a powerful algorithm that allows us to choose how tolerant we are of errors, both through an acceptable error margin(ϵ) and through tuning our tolerance of falling outside that acceptable error rate. Instead of a simple line, it takes a tube of width epsilon(ϵ) which is an intensive tube. Here, the first part of the formula is used to minimize the coefficients whereas the second part of the formula is responsible for tuning the epsilon(ϵ). The graph on the left represents the regression fit line on linear regression models and the graph on the right represents the regression fit line on SVR. The points outside the Intensive Tube(ϵ) are knowns as support vectors which dictate the position of the Intensive Tube(ϵ).

Within one Slack Channel, multiple different conversations might be overlap with each other. Whilst it's normally simple for a human reader to pull them apart this is non-trivial for a computer to do.

Most machine learning algorithms are configured by one or several hyperparameters that must be carefully chosen and often considerably impact performance. To avoid a time consuming and unreproducible manual trial-and-error process to find well-performing hyperparameter configurations, various automatic hyperparameter optimization (HPO) methods, e.g., based on resampling error estimation for supervised machine learning, can be employed. After introducing HPO from a general perspective, this paper reviews important HPO methods such as grid or random search, evolutionary algorithms, Bayesian optimization, Hyperband and racing. It gives practical recommendations regarding important choices to be made when conducting HPO, including the HPO algorithms themselves, performance evaluation, how to combine HPO with ML pipelines, runtime improvements, and parallelization.

What guarantees are possible for solving logistic regression in one pass over a data stream? To answer this question, we present the first data oblivious sketch for logistic regression. Our sketch can be computed in input sparsity time over a turnstile data stream and reduces the size of a $d$-dimensional data set from $n$ to only $\operatorname{poly}(\mu d\log n)$ weighted points, where $\mu$ is a useful parameter which captures the complexity of compressing the data. Solving (weighted) logistic regression on the sketch gives an $O(\log n)$-approximation to the original problem on the full data set. We also show how to obtain an $O(1)$-approximation with slight modifications. Our sketches are fast, simple, easy to implement, and our experiments demonstrate their practicality.

Automated writing evaluation systems can improve students' writing insofar as students attend to the feedback provided and revise their essay drafts in ways aligned with such feedback. Existing research on revision of argumentative writing in such systems, however, has focused on the types of revisions students make (e.g., surface vs. content) rather than the extent to which revisions actually respond to the feedback provided and improve the essay. We introduce an annotation scheme to capture the nature of sentence-level revisions of evidence use and reasoning (the `RER' scheme) and apply it to 5th- and 6th-grade students' argumentative essays. We show that reliable manual annotation can be achieved and that revision annotations correlate with a holistic assessment of essay improvement in line with the feedback provided. Furthermore, we explore the feasibility of automatically classifying revisions according to our scheme.

Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing degrees across covariates, we show that this approach exhibits poor statistical performance when the number of covariates exceeds the number of datasets. For instance, in statistical genetics, we might regress dozens of traits (defining datasets) for thousands of individuals (responses) on up to millions of genetic variants (covariates). When an analyst has more covariates than datasets, we argue that it is often more natural to instead model effects as (1) exchangeable across covariates and (2) correlated to differing degrees across datasets. To this end, we propose a hierarchical model expressing our alternative perspective. We devise an empirical Bayes estimator for learning the degree of correlation between datasets. We develop theory that demonstrates that our method outperforms the classic approach when the number of covariates dominates the number of datasets, and corroborate this result empirically on several high-dimensional multiple regression and classification problems.

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality can lead to erroneous results. We propose an online debiasing estimator to correct these distributional anomalies in least squares estimation. Our proposed method takes advantage of the covariance structure present in the dataset and provides sharper estimates in directions for which more information has accrued. We establish an asymptotic normality property for our proposed online debiasing estimator under mild conditions on the data collection process, and provide asymptotically exact confidence intervals. We additionally prove a minimax lower bound for the adaptive linear regression problem, thereby providing a baseline by which to compare estimators. There are various conditions under which our proposed estimator achieves the minimax lower bound up to logarithmic factors. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.

As the complexity of machine learning (ML) models increases, resulting in a lack of prediction explainability, several methods have been developed to explain a model's behavior in terms of the training data points that most influence the model. However, these methods tend to mark outliers as highly influential points, limiting the insights that practitioners can draw from points that are not representative of the training data. In this work, we take a step towards finding influential training points that also represent the training data well. We first review methods for assigning importance scores to training points. Given importance scores, we propose a method to select a set of DIVerse INfluEntial (DIVINE) training points as a useful explanation of model behavior. As practitioners might not only be interested in finding data points influential with respect to model accuracy, but also with respect to other important metrics, we show how to evaluate training data points on the basis of group fairness. Our method can identify unfairness-inducing training points, which can be removed to improve fairness outcomes. Our quantitative experiments and user studies show that visualizing DIVINE points helps practitioners understand and explain model behavior better than earlier approaches.

What do you do when you see a "You have won a lottery" email? You prefer to report it as'spam' rather than ignoring it. The above image gives an overview of spam filtering. Plenty of emails arrive every day. Some of them go to the spam folder while the rest remain in the primary inbox. Also, emails get classified as primary, social, promotion, updates, forum.

This article introduces and implements the framework of propensity score method from Dehejia and Wahba (1999) "Causal Effects in Non-Experimental Studies: Reevaluating the Evaluation of Training Programs," Journal of the American Statistical Association, Vol. I will briefly go over the theories and then walk through how I implemented the stratification matching step by step. The full Python code is provided at the end of the article. The intuition of propensity score method is: instead of conditioning on the full vector of covariates Xᵢ, which can get difficult when there are many pre-treatment variables and when the treatment and comparison groups are very different, we try to condition on the propensity score estimated with Xᵢ. Propensity score matching works in the same way as covariate matching except that we match on the score instead of the covariates directly.